AgeReplacementPolicy#

class relife.policies.AgeReplacementPolicy(lifetime_model, cf, cp, discounting_rate=0.0)[source]#

Age replacement policy.

Asset is replaced at a fixed age \(a_r\) with cost \(c_p\) or it is replaced upon failure with cost \(c_f\).

Parameters:

lifetime_modelany lifetime distribution or frozen lifetime model: A lifetime model representing the durations between events.
cffloat or 1darray: Costs of failures
cpfloat or 1darray: Costs of preventive replacements
discounting_ratefloat, default is 0.: The discounting rate value used in the exponential discounting function

Attributes:

baseline_modelunivariate parametric lifetime model.: The underlying lifetime model.
discounting_ratefloat: The discounting value.

References

[1]

Mazzuchi, T. A., Van Noortwijk, J. M., & Kallen, M. J. (2007). Maintenance optimization. Encyclopedia of Statistics in Quality and Reliability, 1000-1008.

Methods

`annual_number_of_failures`	The expected annual number of replacements upon failures.
`annual_number_of_replacements`	The expected annual number of replacements.
`asymptotic_expected_equivalent_annual_cost`	The asymtotic expected equivalent annual cost.
`asymptotic_expected_net_present_value`	The asymtotic expected net present value.
`compute_optimal_ar`	Compute the optimal ages of replacement.
`expected_equivalent_annual_cost`	The expected equivalent annual cost.
`expected_net_present_value`	The expected net present value.
`generate_failure_data`	Generate failure data
`get_cf`	Cost of failure.
`get_cp`	Costs of preventive replacements.
`sample`	Renewal data sampling.
`set_cf`
`set_cp`

annual_number_of_failures(nb_years, ar, a0=None)[source]#

The expected annual number of replacements upon failures.

Parameters:

nb_yearsint: The number of years on which the annual number of replacements are projected.
arfloat or np.ndarray: Ages of replacements.
a0float or np.ndarray, optional.: The initial ages.

annual_number_of_replacements(nb_years, ar, a0=None)[source]#

The expected annual number of replacements.

Parameters:

nb_yearsint: The number of years on which the annual number of replacements are projected
arfloat or np.ndarray: Ages of replacements.
a0float or np.ndarray, optional.: The initial ages.

asymptotic_expected_equivalent_annual_cost(ar, a0=None)[source]#

The asymtotic expected equivalent annual cost.

\[\lim_{t\to\infty} q(t)\]

Parameters:

arfloat or np.ndarray: Preventive ages of replacements.
a0float or np.ndarray, optional: Initial ages of the assets.

Returns:

ndarray: The asymptotic expected values.

asymptotic_expected_net_present_value(ar, a0=None)[source]#

The asymtotic expected net present value.

\[\lim_{t\to\infty} z(t)\]

Parameters:

arfloat or np.ndarray: Preventive ages of replacements.
a0float or np.ndarray, optional: Initial ages of the assets.

Returns:

ndarray: The asymptotic expected values.

compute_optimal_ar()[source]#

Compute the optimal ages of replacement.

The optimal ages of replacement depends one the costs, the discounting rate and the underlying lifetime model.

Returns:

outfloat or np.ndarray: Optimal ages of replacements.

discounting_rate#: Base class of age replacement policies.

expected_equivalent_annual_cost(tf, nb_steps, ar, a0=None)[source]#

The expected equivalent annual cost.

\[q(t) = \dfrac{\delta z(t)}{1 - e^{-\delta t}}\]

where :

\(t\) is the time.
\(z(t)\) is the expected net present value at time \(t\).
\(\delta\) is the discounting rate.

Parameters:

tffloat: The final time.
nb_stepsint: The number of steps used to discretized the time.
arfloat or np.ndarray: Preventive ages of replacements.
a0float or np.ndarray, optional: Initial ages of the assets.

Returns:

tuple of two ndarrays: A tuple containing the timeline and the computed values.

expected_net_present_value(tf, nb_steps, ar, a0=None)[source]#

The expected net present value.

\[z(t) = \mathbb{E}(Z_t) = \int_{0}^{\infty}\mathbb{E}(Z_t~|~X_1 = x)dF(x)\]

where :

\(t\) is the time
\(X_1 \sim F\) is the random lifetime of the first asset
\(Z_t\) are the random costs at each time \(t\)
\(\delta\) is the discounting rate

It is computed by solving the renewal equation.

Parameters:

tffloat: The final time.
nb_stepsint: The number of steps used to discretized the time.
arfloat or np.ndarray: Preventive ages of replacements.
a0float or np.ndarray, optional: Initial ages of the assets.

Returns:

tuple of two ndarrays: A tuple containing the timeline and the computed values.

generate_failure_data(nb_samples, time_window, ar, a0=None, seed=None)[source]#

Generate failure data

This function will generate failure data that can be used to fit a lifetime model.

Parameters:

arfloat or np.ndarray: Ages of replacements
nb_samplesint: The number of samples.
time_windowtuple of two floats: Time window in which data are sampled.
seedint, optional: Random seed, by default None.
a0float or np.ndarray or None: Optional, initial ages

Returns:

A dict of time, event, entry and args (covariates)

get_cf()#

Cost of failure.

Returns:

np.ndarray

get_cp()#

Costs of preventive replacements.

Returns:

np.ndarray

sample(nb_samples, time_window, ar, a0=None, seed=None)[source]#

Renewal data sampling.

This function will sample data and encapsulate them in an object.

Parameters:

nb_samplesint: The number of samples.
time_windowtuple of two floats: Time window in which data are sampled.
seedint, optional: Random seed, by default None.